Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.3 - Multiplying and Simplifying Radical Expressions - Exercise Set: 49

Answer

$3x^2y^2\sqrt[3]{3x^2}$

Work Step by Step

Write 81 as $3^4$ to obtain: $=\sqrt[3]{3^4x^8y^6}$ Factor the radicand (expression inside the radical sign) so that at least one factor is a perfect cube, and then simplify to obtain: $=\sqrt[3]{(3^3x^6y^6)\cdot 3x^2} \\=\sqrt[3]{3^3(x^2)^3(y^2)^3 \cdot 3x^2} \\=3x^2y^2\sqrt[3]{3x^2}$
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